{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/negative-momentum-for-improved-game-dynamics","title":"Negative Momentum for Improved Game Dynamics","arxiv_id":"1807.04740","date":"2018-07-12","proceeding":null,"authors":["Gauthier Gidel","Reyhane Askari Hemmat","Mohammad Pezeshki","Remi Lepriol","Gabriel Huang","Simon Lacoste-Julien","Ioannis Mitliagkas"],"abstract":"Games generalize the single-objective optimization paradigm by introducing different objective functions for different players. Differentiable games often proceed by simultaneous or alternating gradient updates. In machine learning, games are gaining new importance through formulations like generative adversarial networks (GANs) and actor-critic systems. However, compared to single-objective optimization, game dynamics are more complex and less understood. In this paper, we analyze gradient-based methods with momentum on simple games. We prove that alternating updates are more stable than simultaneous updates. Next, we show both theoretically and empirically that alternating gradient updates with a negative momentum term achieves convergence in a difficult toy adversarial problem, but also on the notoriously difficult to train saturating GANs.","url_abs":"https://arxiv.org/abs/1807.04740v5","url_pdf":"https://arxiv.org/pdf/1807.04740v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"negative-momentum-for-improved-game-dynamics","repo_url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.04740","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1807.04740"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics","reach":null}],"summary":{"ran_draft_wrong":2,"ran_honours":1,"unverified":1},"by_repo_kind":{"official":{"samples":4,"ran":3,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"551762b39ece9918","entry":"RGB_to_hex","repo":"ReyhaneAskari/negative_momentum_for_improved_game_dynamics","repo_kind":"official","path":"toy_example.py","file_url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics/blob/HEAD/toy_example.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":true,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"551762b39ece9918"}},{"code_sha256_prefix":"d44b926bdac36031","entry":"hex_to_RGB","repo":"ReyhaneAskari/negative_momentum_for_improved_game_dynamics","repo_kind":"official","path":"toy_example.py","file_url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics/blob/HEAD/toy_example.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"well_formed","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"d44b926bdac36031"}},{"code_sha256_prefix":"7859ec20e2a4f4b4","entry":"linear_gradient","repo":"ReyhaneAskari/negative_momentum_for_improved_game_dynamics","repo_kind":"official","path":"toy_example.py","file_url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics/blob/HEAD/toy_example.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7859ec20e2a4f4b4"}},{"code_sha256_prefix":"8165dccb5f7b4b5d","entry":"calc_gradient_penalty","repo":"ReyhaneAskari/negative_momentum_for_improved_game_dynamics","repo_kind":"official","path":"gan_pytorch.py","file_url":"https://github.com/ReyhaneAskari/negative_momentum_for_improved_game_dynamics/blob/HEAD/gan_pytorch.py","link_basis":"first_harvest_node","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"8165dccb5f7b4b5d"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}